Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system

doi:10.1051/m2an/2020015

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	Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system
	Gong, Wei 1,2; Hu, Weiwei 3; Mateos, Mariano 4; Singler, John R.5; Zhang, Yangwen 6
	2020-11-03
发表期刊	ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
ISSN	0764-583X
卷号	54 期号:6 页码:2229-2264
摘要	We consider an unconstrained tangential Dirichlet boundary control problem for the Stokes equations with an L-2 penalty on the boundary control. The contribution of this paper is twofold. First, we obtain well-posedness and regularity results for the tangential Dirichlet control problem on a convex polygonal domain. The analysis contains new features not found in similar Dirichlet control problems for the Poisson equation; an interesting result is that the optimal control has higher local regularity on the individual edges of the domain compared to the global regularity on the entire boundary. Second, we propose and analyze a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For convex polygonal domains, our theoretical convergence rate for the control is optimal with respect to the global regularity on the entire boundary. We present numerical experiments to demonstrate the performance of the HDG method.
关键词	Tangential Dirichlet boundary control Stokes equations hybridizable discontinuous Galerkin method
DOI	10.1051/m2an/2020015
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11671391] ; National Natural Science Foundation of China[91530204] ; National Key Basic Research Program[2018YFB0704304] ; NSF[DMS-1813570] ; Spanish Ministerio de Economia y Competitividad[MTM2017-83185-P] ; National Science Foundation[DMS-1217122] ; US National Science Foundation (NSF)[DMS-1217122] ; US National Science Foundation (NSF)[DMS-1619904]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000585906800003
出版者	EDP SCIENCES S A
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52428
专题	中国科学院数学与系统科学研究院
通讯作者	Singler, John R.
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, NCMIS, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 3.Univ Georgia, Dept Math, Athens, GA 30602 USA 4.Univ Oviedo, Dept Matemat, Campus Gijon, Gijon, Spain 5.Missouri Univ Sci & Technol, Dept Math & Stat, Rolla, MO 65409 USA 6.Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
推荐引用方式 GB/T 7714	Gong, Wei,Hu, Weiwei,Mateos, Mariano,et al. Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,2020,54(6):2229-2264.
APA	Gong, Wei,Hu, Weiwei,Mateos, Mariano,Singler, John R.,&Zhang, Yangwen.(2020).Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system.ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE,54(6),2229-2264.
MLA	Gong, Wei,et al."Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system".ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE 54.6(2020):2229-2264.